Attachment assemblies are known by which objects such as wire handles can be attached to surfaces. One such type of attachment assembly comprises a flexible strap, a fastener comprising portions adapted for releasable engagement attached on opposite ends of the strap, and means for attaching the strap to a surface. Typically the strap is attached to a surface and is then wrapped around the object to be held in place and the fastener portions are engaged. In known prior art fastener assemblies of this type, however, forces tending to dislodge the object from the fastener assembly tend to peel apart the fastener portions, which peeling is the easiest way of separating the fastener portions. Thus the fastener assembly may not be as secure as is desired due to the limited amount of resistance to such peel forces that can easily be designed into many fasteners.